# Electric power – problems and solutions

28 Electric power – problems and solutions

1. Calculate the electric current of a 10 Watt lamp designed for 12 Volt.

Known :

Power (P) = 10 Watt

Voltage (V) = 220 Volt

Wanted : Electric current

Solution :

Lamp power = 10 Watt = 10 Joule/second

The equation below shows the relation between the electric power (P), electric potential (V) and electric current (I) stated in formula below :

P = V I

Electric current :

I = P / V = 10 / 220 = 1/22 = 0.045 Ampere

2. Calculate the electric power according to the electric circuit below.

Known :

Resistor 1 (R1) = 6 Ω

Resistor 2 (R2) = 6 Ω

Electric voltage (V) = 24 Volt

Wanted : Electric power

Solution :

Equivalent resistor :

R1 and R2 are connected in series. The equivalent resistor :

R = R1 + R2 = 6 Ω + 6 Ω = 12 Ω

The electric current :

I = V/R = 24/12 = 2 Ampere

Electric power :

P = V I = (24)(2) = 48 Watt = 48 Joule/second

3. Calculate the electric current of a 3 kiloWatt designed for 150 Volt.

Known :

Electric power (P) = 3 kiloWatt = 3000 Watt

Electric voltage (V) = 150 Volt

Wanted : Electric current (I)

Solution :

Relation of the electric power (P), electric potential (V) and electric current (I) stated in formula below :

P = V I

The electric current :

I = P / V

I = 3000 Watt / 150 Volt

I = 20 Ampere

4. Calculate the power for a $$10\,\Omega$$ resistor with a $$5\,A$$ current.
Solution: $$P = I^2 R = 5^2 \times 10 = 250\,W$$

5. Determine the power for a circuit with $$12\,V$$ and $$4\,\Omega$$ resistance.
Solution: $$P = \frac{V^2}{R} = \frac{12^2}{4} = 36\,W$$

6. A $$60\,W$$ bulb operates for $$3\,h$$. Calculate the energy consumed.
Solution: $$E = Pt = 60 \times 3 = 180\,Wh = 0.18\,kWh$$

7. Calculate the current for a $$200\,W$$ appliance on a $$100\,V$$ supply.
Solution: $$I = \frac{P}{V} = \frac{200}{100} = 2\,A$$

8. Find the resistance of a heater that uses $$1200\,W$$ at $$240\,V$$.
Solution: $$R = \frac{V^2}{P} = \frac{240^2}{1200} = 48\,\Omega$$

9. A $$9\,V$$ battery is connected to a $$3\,\Omega$$ resistor. Find the power dissipated.
Solution: $$P = \frac{V^2}{R} = \frac{9^2}{3} = 27\,W$$

10. Calculate the power in a $$10\,\Omega$$ resistor with a $$100\,V$$ supply.
Solution: $$P = \frac{V^2}{R} = \frac{100^2}{10} = 1000\,W$$

11. Determine the voltage required to dissipate $$50\,W$$ in a $$10\,\Omega$$ resistor.
Solution: $$V = \sqrt{PR} = \sqrt{50 \times 10} = 22.36\,V$$

12. A motor uses $$1500\,W$$ and runs for $$4\,h$$. Find the energy consumed.
Solution: $$E = Pt = 1500 \times 4 = 6000\,Wh = 6\,kWh$$

13. Find the current of a $$240\,V$$ supply if the power is $$1200\,W$$.
Solution: $$I = \frac{P}{V} = \frac{1200}{240} = 5\,A$$

14. Calculate the resistance for a $$100\,W$$ bulb operating at $$200\,V$$.
Solution: $$R = \frac{V^2}{P} = \frac{200^2}{100} = 400\,\Omega$$

15. Determine the power in a $$3\,A$$ circuit with a $$15\,\Omega$$ resistor.
Solution: $$P = I^2 R = 3^2 \times 15 = 135\,W$$

16. Calculate the voltage needed to dissipate $$100\,W$$ in a $$20\,\Omega$$ resistor.
Solution: $$V = \sqrt{PR} = \sqrt{100 \times 20} = 44.72\,V$$

17. Find the energy consumed by a $$300\,W$$ fan running for $$2\,h$$.
Solution: $$E = Pt = 300 \times 2 = 600\,Wh = 0.6\,kWh$$

18. Calculate the current in a circuit with $$1000\,W$$ power and $$250\,V$$ voltage.
Solution: $$I = \frac{P}{V} = \frac{1000}{250} = 4\,A$$

19. Determine the resistance of a $$400\,W$$ toaster operating at $$100\,V$$.
Solution: $$R = \frac{V^2}{P} = \frac{100^2}{400} = 25\,\Omega$$

20. Find the power for a $$20\,V$$ voltage across a $$5\,\Omega$$ resistor.
Solution: $$P = \frac{V^2}{R} = \frac{20^2}{5} = 80\,W$$

21. Calculate the voltage needed to provide $$200\,W$$ to a $$25\,\Omega$$ resistor.
Solution: $$V = \sqrt{PR} = \sqrt{200 \times 25} = 50\,V$$

22. Determine the energy consumed by a $$500\,W$$ machine running for $$5\,h$$.
Solution: $$E = Pt = 500 \times 5 = 2500\,Wh = 2.5\,kWh$$

23. Find the current for a $$60\,W$$ bulb operating at $$120\,V$$.
Solution: $$I = \frac{P}{V} = \frac{60}{120} = 0.5\,A$$

24. Calculate the resistance for a $$40\,W$$ lamp running at $$20\,V$$.
Solution: $$R = \frac{V^2}{P} = \frac{20^2}{40} = 10\,\Omega$$

25. Determine the power in a $$5\,A$$ circuit with a $$12\,\Omega$$ resistor.
Solution: $$P = I^2 R = 5^2 \times 12 = 300\,W$$

26. Calculate the voltage required to deliver $$150\,W$$ to a $$15\,\Omega$$ resistor.
Solution: $$V = \sqrt{PR} = \sqrt{150 \times 15} = 61.24\,V$$

27. Find the energy consumed by a $$800\,W$$ air conditioner running for $$3\,h$$.
Solution: $$E = Pt = 800 \times 3 = 2400\,Wh = 2.4\,kWh$$

28. Determine the current in a circuit with $$500\,W$$ power and $$125\,V$$ voltage.
Solution: $$I = \frac{P}{V} = \frac{500}{125} = 4\,A$$